Atkin-Lehner |
2+ 3+ 19- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
83448a |
Isogeny class |
Conductor |
83448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-110960471808 = -1 · 28 · 39 · 192 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 0 4 0 2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-135,-16038] |
[a1,a2,a3,a4,a6] |
j |
-54000/22021 |
j-invariant |
L |
3.7851624615303 |
L(r)(E,1)/r! |
Ω |
0.47314530767238 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
83448g1 |
Quadratic twists by: -3 |